It is worth noting that WRW can sometimes significantly outperform UIS. This is the case in Fig. REF (d), where UIS is equivalent to WIS with \(w\!=\!1\) .
Because no walk can mix faster than UIS (that is independent and thus has perfect mixing), improving the mixing time alone [1]}, [2]}, [3]}, [4]} cannot achieve the potential gains of stratification, in general.
